Nontrivial solutions for a $(p,q)$-Kirchhoff type system with concave-convex nonlinearities on locally finite graphs

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Yu, Zhangyi, Xie, Junping, Zhang, Xingyong
Formato: Preprint
Publicado: 2024
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866912175802548224
author Yu, Zhangyi
Xie, Junping
Zhang, Xingyong
author_facet Yu, Zhangyi
Xie, Junping
Zhang, Xingyong
contents By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a $(p,q)$-Kirchhoff elliptic system with the Dirichlet boundary conditions and perturbation terms on a locally weighted and connected finite graph $G=(V,E)$.We also present a necessary condition of the existence of semi-trivial solutions for the system. Moreover, by using Ekeland's variational principle and Clark's Theorem, respectively, we prove that the system has at least one or multiple semi-trivial solutions when the perturbation terms satisfy different assumptions. Finally, we present a nonexistence result of solutions.
format Preprint
id arxiv_https___arxiv_org_abs_2408_02041
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Nontrivial solutions for a $(p,q)$-Kirchhoff type system with concave-convex nonlinearities on locally finite graphs
Yu, Zhangyi
Xie, Junping
Zhang, Xingyong
Analysis of PDEs
By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a $(p,q)$-Kirchhoff elliptic system with the Dirichlet boundary conditions and perturbation terms on a locally weighted and connected finite graph $G=(V,E)$.We also present a necessary condition of the existence of semi-trivial solutions for the system. Moreover, by using Ekeland's variational principle and Clark's Theorem, respectively, we prove that the system has at least one or multiple semi-trivial solutions when the perturbation terms satisfy different assumptions. Finally, we present a nonexistence result of solutions.
title Nontrivial solutions for a $(p,q)$-Kirchhoff type system with concave-convex nonlinearities on locally finite graphs
topic Analysis of PDEs
url https://arxiv.org/abs/2408.02041